Isolated many-body quantum systems far from equilibrium: Relaxation process and thermalization

Abstract

Equilibration of an isolated quantum many-body system Phys. Today Abstract. We present an overview of our recent numerical and analytical results on the dynamics of isolated interacting quantum systems that are taken far from equilibrium by an abrupt perturbation. The studies are carried out on one-dimensional systems of spins-1/2, which are paradigmatic models of many-body quantum systems. Our results show the role of the interplay between the initial state and the post-perturbation Hamiltonian in the relaxation process, the size of the fluctuations after equilibration, and the viability of thermalization.

Analytical expressions for the evolution of many-body quantum systems quenched far from equilibrium

“…The perturbation that starts the evolution of the initial state is very strong, it consists of quenching J from 0 to 1. In the limit of strong perturbation, the LDOS and DOS have similar shapes [1][2][3][4]. However, in contrast to FRM, the DOS of systems with two-body interactions, as in Eq.…”

“…Because of this, our studies concentrate on initial states that have energy E n 0 very close to the middle of the spectrum. The Fourier transform of a Gaussian LDOS results in the Gaussian decay of the survival probability, e −ω 2 n 0 t 2 , where ω n 0 is the width of the LDOS [1][2][3][4][5]27]. But when doing the Fourier transform, we should also take into account the unavoidable presence of energy bounds in the spectrum.…”

“…Initially, the decay of the OTOC is controlled by J 4 1 (εt)/(εt) 4 , which results in a power-law decay ∝ 1/t 6 . At long times, the correlation hole develops due to b 2 2 (Dt/2π), that is, again due to the two-level form factor, but in a different functional form.…”

“…Since 2014, we have been searching for expressions that could describe the dynamics of many-body quantum systems out of equilibrium [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. We started our studies with a very simple quantity, referred to as the survival probability.…”

Quantum chaos and thermalization in isolated systems of interacting particles

“…Since the survival probability is the Fourier transform of the strength function, the shape and filling of the latter regulate the decay of the first. This allows for the following conclusions [215,216,51,214,87,217,218], which are illustrated below: (i) the decay for integrable and chaotic Hamiltonians may be very similar; (ii) it may be exponential, Gaussian and even faster than Gaussian, the fastest behavior being limited by the energy-time uncertainty relation; (iii) it slows down as the energy of the initial state moves away from the middle of the spectrum.…”